Brake system providing limited antiskid control during a backup mode of operation

ABSTRACT

A brake system for a vehicle is disclosed and includes an energy storage device configured to store and discharge energy, a plurality of wheels, one or more processors operatively coupled to the energy storage device, and a memory coupled to the one or more processors. The memory stores data comprising a database and program code that, when executed by the one or more processors, causes the brake system to determine the brake system is operating in a backup mode of operation. In response to determining the brake system is operating in the backup mode of operation, the brake system calculates a dynamic slip of the plurality of wheels. The brake system is caused to determine a slip error by comparing the dynamic slip with a target slip value of the plurality of wheels. The brake system is also caused to calculate an antiskid command based on the slip error.

INTRODUCTION

The present disclosure relates to a brake system for a vehicle. Moreparticularly, the present disclosure is directed towards a brake systemthat employs a limited antiskid control strategy during a backup mode ofoperation to conserve energy stored within an energy storage device.

BACKGROUND

Aircraft brakes are used in a variety of situations. For example,aircraft brakes are used to slow the aircraft down during landing rollalong a runway. Aircraft brakes may also be used during ground handlingoperations such as, for example, taxiing, steering, and parking.

Hydraulic aircraft brake systems include an accumulator that storeshydraulic braking fluid under pressure. The accumulator is used as aredundant pressure source as well as a backup source of fluid energy.Specifically, the braking accumulator is primarily used to providesustained hydraulic pressure after the active hydraulic system isdepressurized, and is also used as a backup source of energy in theevent there is a loss of hydraulic pressure within the brake system orif the aircraft's hydraulic power system becomes inoperable. However,the accumulator is only able to store a limited amount of hydraulicbrake fluid. Accordingly, the hydraulic fluid level and pressure of theaccumulator is depleted each time brake pressure is applied andreleased. For example, some accumulators are sized to provide enoughhydraulic fluid for only about six to eight brake applications.Furthermore, with each brake application, the accumulator pressure,accumulator fluid volume, and maximum braking pressure decrease. Oncethe accumulator is emptied, then the brakes may no longer be applied toreduce the speed of the aircraft.

In an effort to preserve the hydraulic fluid stored within theaccumulator, some functions of the brake system may not be availablewhen the accumulator is being used as a backup source of fluid energy.For example, sometimes the brake system may only use pedal brake control(i.e., brake input by a pilot), without antiskid control. Antiskidcontrol provides skid protection by momentarily relieving the hydraulicpressure provided to a wheel, which results in the wheel being able torotate and avoid a skid. Omitting antiskid control may create issues ifthe aircraft is traveling along a slippery surface, such as an icyrunway. Alternatively, in another approach, the brake system may stillprovide antiskid control when the accumulator is used as a backup sourceof fluid energy. However, this may result in the accumulator beingemptied relatively quickly if the brakes are released excessivelybecause of skid protection.

SUMMARY

According to several aspects, a brake system for a vehicle is disclosed.The brake system includes an energy storage device configured to storeand discharge energy, a plurality of wheels, one or more processorsoperatively coupled to the energy storage device and in electricalcommunication with the plurality of wheels, and a memory coupled to theone or more processors. The memory stories data comprising a databaseand program code that, when executed by the one or more processors,causes the brake system to determine the brake system is operating in abackup mode of operation. In response to determining the brake system isoperating in the backup mode of operation, the brake system is caused tocalculate a dynamic slip of the plurality of wheels. The brake system isalso caused to determine a slip error by comparing the dynamic slip witha target slip value of the plurality of wheels, where the target slipvalue is offset from an ideal slip value of the plurality of wheels andresults in a reduced braking efficiency of the brake system. The brakesystem is also caused to calculate an antiskid command based on the sliperror, where the antiskid command reduces an amount of brake pressureapplied to the plurality of wheels.

According to another aspect, an aircraft is disclosed. The aircraftincludes a brake system including a plurality of wheels and anaccumulator, where the accumulator is configured to store and dischargefluid energy as a pressurized hydraulic brake fluid. The aircraft alsoincludes one or more processors operatively coupled to the accumulatorand in electrical communication with the plurality of wheels and amemory coupled to the one or more processors. The memory stores datacomprising a database and program code that, when executed by the one ormore processors, causes the brake system to determine the brake systemis operating in a backup mode of operation, where the backup mode ofoperation conserves the fluid energy stored in the accumulator. Inresponse to determining the brake system is operating in the backup modeof operation, the brake system is caused to calculate a dynamic slip ofthe plurality of wheels. The brake system is further caused to determinea slip error by comparing the dynamic slip with a target slip value ofthe plurality of wheels, where the target slip value is offset from anideal slip value of the plurality of wheels and results in a reducedbraking efficiency of the brake system. The brake system is also causedto calculate an antiskid command based on the slip error, where theantiskid command reduces an amount of brake pressure applied to theplurality of wheels.

In still another aspect, a method of determining an antiskid commandduring a backup mode of operation for a brake system of a vehicle isdisclosed. The brake system includes a plurality of wheels and energystorage device configured to store and discharge energy. The methodincludes determining, by a computer, the brake system is operating in abackup mode of operation. In response to determining the brake system isoperating in the backup mode of operation, the method includescalculating, by the computer, a dynamic slip of the plurality of wheels.The method also includes determining a slip error by comparing thedynamic slip with a target slip value, where the target slip value isless than an ideal slip value and results in a reduction in brakingefficiency when compared to the ideal slip value. Finally, the methodincludes calculating an antiskid command based on the slip error, wherethe antiskid command reduces an amount of brake pressure applied to theplurality of wheels.

The features, functions, and advantages that have been discussed may beachieved independently in various embodiments or may be combined inother embodiments further details of which can be seen with reference tothe following description and drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings described herein are for illustration purposes only and arenot intended to limit the scope of the present disclosure in any way.

FIG. 1 is a schematic diagram of a brake system including an energystorage device in the form of an accumulator, according to an exemplaryembodiment;

FIG. 2 is a block diagram illustrating an approach for determining anantiskid command when the brake system is operating in a backup mode ofoperation, according to an exemplary embodiment;

FIG. 3 is an exemplary mu-slip curve illustrating an ideal slip pointand a target slip point, according to an exemplary embodiment;

FIG. 4 is a process flow diagram illustrating a method for determiningthe antiskid command based on the system shown in FIG. 2, according toan exemplary embodiment;

FIG. 5 is a block diagram illustrating an alternative approach fordetermining an antiskid command when the brake system is operating inthe backup mode, according to an exemplary embodiment;

FIG. 6A is a graph illustrating the brake pressure of an observer wheelshown in FIG. 5 undergoing a skid condition, according to an exemplaryembodiment;

FIG. 6B is a graph illustrating brake torque of the observer wheel,according to an exemplary embodiment;

FIG. 6C is a graph illustrating the wheel speed of the observer wheelcompared to the actual vehicle speed, according to an exemplaryembodiment;

FIG. 6D is a mu-slip curve of the observer wheel undergoing the skid,according to an exemplary embodiment;

FIG. 7 is a process flow diagram illustrating another method fordetermining the brake pressure, according to an exemplary embodiment;and

FIG. 8 is an illustration of a computer system used by the brake systemof FIG. 1 according to an exemplary embodiment.

DETAILED DESCRIPTION

The disclosure is directed towards a brake system for a vehicle, wherethe brake system includes an energy storage device. During a backup modeof operation, the energy storage device is used to supply energy to thebrake system. The brake system conserves an amount of energy that isstored within the energy storage device during the backup mode ofoperation. Specifically, a control module of the brake system determinesan antiskid command that represents a reduction in brake pressureapplied to the wheels of the vehicle. The antiskid command is calculatedbased on an error between a dynamic slip of the wheels and a target slipvalue of the wheels. The target slip value is offset from an ideal slipvalue of the wheels, and results in a reduced stopping efficiency of thebrake system. However, since the target slip results in a reduced amountof brake pressure applied to the wheels, the brake system consumes lessenergy from the energy storage device each time brakes are applied toreduce the speed of the vehicle.

The following description is merely exemplary in nature and is notintended to limit the present disclosure, application, or uses.

Referring to FIG. 1, a schematic diagram of a vehicle 10 having a brakesystem 18 is illustrated. The brake system 18 includes a brake pedalcommand 20, a control module 22, a plurality of wheels 24 (only onewheel 24 is shown in FIG. 1), a valve 26, a one-way or check valve 28,an energy storage device 30, a piston cylinder assembly 32, and a brakestack 34. The control module 22 is in electronic communication with thebrake pedal command 20 and the valve 26. The valve 26 fluidly connectsthe piston cylinder assembly 32 with the energy storage device 30 whenthe brake system 18 is operating in a backup mode of operation, which isexplained in greater detail below. The energy storage device 30 is anytype of device configured to store and discharge energy when required bythe brake system 18. For example, in the embodiment as shown, the energystorage device 30 is an accumulator 30A configured to store anddischarge energy as a pressurized hydraulic brake fluid. The energystorage device 30 provides a source of backup energy when the brakesystem 18 loses active hydraulic power. As explained below, when theenergy storage device 30 is used as a source of backup energy, the brakesystem 18 limits the antiskid control employed by the brake system 18 toconserve the energy stored in the energy storage device 30.

In the non-limiting embodiment as shown in FIG. 1, the brake system 18employs a hydraulic brake fluid and the energy storage device 30 is theaccumulator 30A. The accumulator 30A configured to store and dischargefluid energy as a pressurized hydraulic brake fluid. Some examples ofthe accumulator 30A include, but are not limited to, a compressed gasaccumulator (also referred to as a bladder-type accumulator) or a springaccumulator. Although FIG. 1 illustrates a brake system 18 employinghydraulic brake fluid, it is to be appreciated that the brake system 18is not limited to hydraulic systems. For example, in another embodiment,the brake system 18 is an electronic brake system. Furthermore, theenergy storage device 30 is not limited to an accumulator 30A. Instead,the energy storage device 30 includes any type of device configured tostore and release energy such as, but not limited to, a battery, acapacitor, or a flywheel.

In one embodiment, the vehicle 10 is an aircraft 182 (seen in FIG. 5)including a hydraulic brake system 18 and the accumulator 30A. However,it is to be appreciated that the brake system 18 may also be employed inother types of vehicles that operate under a limited power source (i.e.,the energy storage device 30) as well. It is also to be appreciated thatwhile FIG. 1 illustrates only a single brake system 18, an aircraft mayactually include multiple brake systems 18. For example, an aircraft mayinclude separate brake systems that correspond to the left and rightwheels of an aircraft.

The brake system 18 also includes a supply pressure conduit 40, a returnpressure conduit 42 and a brake line conduit 44. The supply pressureconduit 40 is fluidly connected to the check valve 28 and the energystorage device 30, and the brake line conduit 44 is fluidly connected tothe piston cylinder assembly 32. The valve 26 is configured to fluidlyconnect the brake line conduit 44 with either the supply pressureconduit 40 or the return pressure conduit 42. When the valve 26 fluidlyconnects the supply pressure conduit 40 with the brake line conduit 44,pressurized brake fluid is supplied to piston cylinder assembly 32. Thecheck valve 28 prevents brake fluid from flowing in a direction oppositethe valve 26.

The brake stack 34 includes one or more rotors 50 and one or morestators 52, where the rotors 50 rotate in concert with the wheels 24.The piston cylinder assembly 32 includes a piston 54, a cylinder 56, anda biasing element 66, where the piston 54 is configured to translateback and forth in a linear motion within the cylinder 56. In theembodiment as shown, the biasing element 66 is a coil spring. When thevalve 26 fluidly connects the supply pressure conduit 40 with the brakeline conduit 44, pressurized brake fluid is supplied to piston cylinderassembly 32 and causes the piston 54 to overcome a biasing force exertedby the biasing element 66. Once the piston 54 overcomes the biasingforce, the piston 54 translates within the cylinder 56 in a directiontowards the brake stack 34. The piston 54 continues to travel towardsthe brake stack 34 until an end portion 60 of the piston 54 abutsagainst and exerts a compressive force upon the brake stack 34. When thebrake stack 34 is compressed, friction forces are developed between therotors 50 and stators 52 that resist rotation of the wheels 24.

The brake system 18 further includes a wheel speed sensor 70, a brakepressure transducer 72, and an accumulator pressure transducer 74 thatare each in electrical communication with the control module 22. Thewheel speed sensor 70 measures a rotational speed of the wheels 24,which is referred to as the wheel speed 80. The brake pressuretransducer 72 measures the fluid pressure within the brake line conduit44 and generates a proportional electrical signal that is referred to asa brake pressure signal 82. The accumulator pressure transducer 74measures the fluid pressure of the energy storage device 30 (i.e., theaccumulator 30A), and generates an accumulator pressure signal that isreferred to as an energy storage level 84. This is because a decrease inthe accumulator pressure indicates a decrease in the amount of energystored within the accumulator 30A.

The control module 22 receives as input the wheel speed 80, the brakepressure signal 82, and the energy storage level 84. The control module22 also receives an input command 86 from the brake pedal command 20.The input command 86 represents an amount of braking requested by thebrake system 18. For example, if the brake pedal command 20 is a brakepedal, then an operator depresses the brake pedal manually to create theinput command 86 received by the control module 22. The control module22 determines a brake pressure command 88 that is sent to the valve 26.The brake pressure command 88 instructs the valve 26 to either increaseor decrease the fluid pressure supplied to the brake system 18.Specifically, the valve 26 fluidly connects the supply pressure conduit40 and the energy storage device 30 to the brake line conduit 44 toincrease the fluid pressure supplied to the brake system. The valve 26fluidly connects the return pressure conduit 42 to the brake lineconduit 44 to decrease the fluid pressure supposed to the brake system18. For example, in one non-limiting embodiment, the valve 26 is a servovalve and the brake pressure command 88 is a milliamp signal.

The backup mode of operation of the brake system 18 is now described.Specifically, when the brake system 18 experiences a loss of activepower, then the control module 22 executes the backup mode of operation.Specifically, the control module 22 is operatively connected to theenergy storage device 30. During the backup mode of operation, thecontrol module 22 instructs the valve 26 to fluidly connect the energystorage device 30 to the brake line conduit 44. For example, if thebrake system 18 employs a hydraulic brake fluid, then the accumulator30A is used as a backup source of fluid energy in the event there is aloss of active supply hydraulic pressure within the brake system 18.

It is to be appreciated the energy storage device 30 only contains afixed or limited amount of energy such as, for example, hydraulic brakefluid. Similarly, if the brake system 18 is an electrical brake system,then a battery may only contain a limited amount of chemical energy thatis readily converted into electrical power. The disclosed backup mode ofoperation conserves the amount of energy stored in the energy storagedevice 30 by instructing the brake system 18 to execute a limitedantiskid control strategy. Specifically, the backup mode of operationlimits the dynamic change of fluid pressure supplied to the brake system18, which in turn conserves the amount of energy (i.e., hydraulic brakefluid, chemical energy, etc.) stored in the energy storage device 30.

FIG. 2 is a block diagram 100 illustrating one approach to calculate anantiskid command 90 by the control module 22. The antiskid command 90 isderived from the wheel speed 80. The antiskid command 90 reduces anamount of brake pressure applied to the plurality of wheels 24 andprovides antiskid control as the vehicle 10 comes to a stop. However, itis to be appreciated that the antiskid command 90 provides a reducedamount of antiskid control when compared to a conventional antiskidsystem. Turning back to FIG. 2, the block diagram 100 includes a slipcomputational block 103, a target slip block 104, an integrator gain aproportional gain k_(p), and an integrator 108.

Referring to FIGS. 1 and 2, the control module 22 dynamically calculatesthe brake pressure command 88 once the wheels 24 of the vehicle 10rotate along a surface. For example, if the vehicle 10 is an aircraft,then the control module 22 dynamically calculates the brake pressurecommand 88 once the wheels 24 rotate along a runway surface. The controlmodule 22 receives as input or determines a wheel frequency ω based onthe wheel speed 80 as the wheels 24 rotate along a ground surface. Thecontrol module 22 also receives as input an actual speed 102. Forexample, if the vehicle 10 is an aircraft, then the actual speed 102 isa ground speed signal.

Continuing to refer to FIGS. A and 2, the slip computational block 103calculates a dynamic slip 112 of the plurality of wheels 24 based on thewheel frequency co and the actual speed 102. Specifically, in anembodiment, the slip computational block 103 calculates the dynamic slip112 based on Equation 1, which is:

${{Dynamic}\mspace{14mu}{slip}\mspace{14mu} 112} = \frac{( {{{actual}\mspace{14mu}{speed}\mspace{14mu}{signal}\mspace{14mu} 102} - {R*\omega}} )}{{actual}\mspace{14mu}{speed}\mspace{14mu}{signal}\mspace{14mu} 102}$where R represents a tire rolling radius of the tires 94 of theplurality of wheels 24 of the vehicle 10. The dynamic slip 112 is thensent to a summing junction 114. The summing junction 114 receives asinput the dynamic slip 112 and a target slip value 116 of the pluralityof wheels 24. The target slip value 116 may also be referred to as aslip offset as well, since the target slip value 116 is offset from anideal slip value of the plurality of wheels 24. The target slip value116 results in a reduction in braking efficiency of the brake system 18when compared to the ideal slip value, which is explained below andshown in FIG. 3. It is to be appreciated that the target slip value 116is a fixed value, where the fixed value is based on a type of tire 94installed on the plurality of wheels 24. The type of tire 94 depends oncharacteristics such as, for example, belt construction and sidewallconstruction, where belt construction refers to either a radial orcross-ply construction. Accordingly, if the specific type of tires 94installed on the wheels 24 change, then the target slip value 116 isupdated.

FIG. 3 illustrates an exemplary mu-slip curve 130. It is to beappreciated that the mu-slip curve 130 is shown for purposes ofexplanation, and the control module 22 may not have knowledge of themu-slip curve 130. The specific mu-slip curve profile 132 is based onthe specific type of tires 94 (FIG. 1). The mu-slip curve 130 includesan x-axis that represents tire slip and a y-axis that represents brakingefficiency. In the non-limiting example as shown in FIG. 3, an idealslip point 134 represents the point along the mu-slip curve 130 thatresults in a maximum percentage of braking efficiency. In an embodiment,the ideal slip point 134 results in about 12% braking efficiency. Atarget slip point 136 is offset from the ideal slip point 134. Forexample, in the embodiment as shown, the target slip point 136correlates to about 8-10% braking efficiency. The difference between theideal slip point 134 and the target slip point 136 is referred to as areduction in braking efficiency 140.

Referring to FIGS. 1 and 3, it is to be appreciated that the reductionin braking efficiency 140 results in a reduced stopping efficiency ofthe brake system 18. In other words, the target slip point 136 resultsin reduced performance parameters as the brake system 18 brings thevehicle 10 to a stop. Some examples of brake performance parametersinclude, but are not limited to, stopping distance and time. If avehicle 10 takes too long or requires too much distance when coming to astop, this may create adverse conditions. Accordingly, the controlmodule 22 selects the target slip point 136 that results in the brakesystem 18 having the vehicle 10 come to a stop within a threshold timeand a threshold distance. For example, if the vehicle 10 is an aircraft,then the threshold time and the threshold distance ensure that theaircraft remains on the runway during landing. Accordingly, the targetslip value 116 seen in FIG. 2 represents an increase in stoppingdistance and stopping time of the brake system 18 when compared to theideal slip value. However, the target slip value 116 also results in thebrake system 18 consuming less energy from the energy storage device 30each time the brake system 18 is applied.

Referring to FIGS. 1 and 2, the summing junction 114 determines a sliperror 148 by comparing the dynamic slip 112 with the target slip value116, where the slip error 148 is the difference between the dynamic slip112 and the target slip. The slip error 148 is then applied to aproportional-integral (PI) controller 150 to determine the antiskidcommand 90. The PI controller 150 includes the proportional gain k_(p),the integral gain k_(i), and the integrator 108.

Combining the proportional gain k_(p) with the slip error 148 results ina proportional increase in a value of the antiskid command 90 as theslip error 148 remains constant. Higher values of the proportional gaink_(p) result in removing the slip error 148 from the antiskid command 90at a faster rate. The proportional gain k_(p) is based on brake systemdynamics (i.e., valves, tires, and hydraulics) and structural dynamicsof the vehicle 10. If the vehicle 10 is an aircraft, then theproportional gain k_(p) is also based on aerodynamics and a groundreaction. The ground reaction refers to friction and vertical forceapplied upon the aircraft. The control module 22 combines the slip error148 with the proportional gain k_(p), which results in a proportionalvalue 160 that is sent to a summing junction 162.

The integral gain k_(i) is a fixed value stored in a memory 1034 (FIG.8) of the control module 22. Alternatively, the proportional gain k_(p)is a function or is determined based on a look-up table. The integralgain k_(i) results in a reduced steady-state rate of slip error 148 fora given response of the brake system 18. A higher value of the integralgain k_(i) results in removing the slip error 148 from the antiskidcommand 90 at a faster rate. It is to be appreciated that increasing theintegral gain k_(i) allows for the brake system 18 to adjust to skiddingquickly, without the need to command the proportional gain k_(p)constantly. The control module 22 combines the slip error 148 with theintegral gain k_(i), which results in a first integral value 164. Thefirst integral value 164 is integrated by the integrator 108, and theresulting second integral value 168 is sent to the summing junction 162.

The summing junction 162 combines the proportional value 160 and thesecond integral value 168 together, which results in the antiskidcommand 90. As seen in FIG. 3, the brake pressure command 88 isdetermined based on the input command 86 and the antiskid command 90.Specifically, the control module 22 determines the brake pressurecommand 88 based on a difference between the antiskid command 90 and theinput command 86, where the brake pressure command 88 indicates anamount of compressive force exerted upon the plurality of wheels 24 ofthe vehicle 10 by the brake stack 34.

Referring now to FIG. 4, an exemplary process flow diagram illustratinga method 200 of determining the antiskid command 90 during the backupmode of operation is shown. Referring to FIGS. 1, 2, and 4, the method200 begins at decision block 202. In decision block 202, the controlmodule 22 determines if the brake system 18 is operating in the backupmode of operation. As mentioned above, the backup mode of operationconserves energy stored in the energy storage device. If the brakesystem 18 is operating in the backup mode of operation, then the method200 may then proceed to block 204.

In block 204, in response to determining the brake system 18 isoperating in the backup mode of operation, the control module 22calculates the dynamic slip 112 (seen in FIG. 2) of the plurality ofwheels 24. The method 200 may then proceed to block 206.

In block 206, the control module 22 determines the slip error 148 bycomparing the dynamic slip 112 with the target slip value 116, where thetarget slip value 116 is less than the ideal slip value of the pluralityof wheels 24 and results in a reduction in braking efficiency whencompared to the ideal slip value.

In an embodiment, the control module 22 determines the slip error 148 inblock 206A. Specifically, in block 206A, the control module 22determines the slip error 148 based on the wheel frequency ω of theplurality of wheels 24 and the actual speed 102 of the vehicle 10. In anembodiment, the control module determines the slip error 148 based onEquation 1, which is shown above. The method 200 may then proceed toblock 208.

Referring specifically to FIGS. 2 and 4, in block 208A the controlmodule 22 combines the slip error 148 with the proportional gain k_(p),which results in the proportional value 160. As mentioned above,combining the proportional gain k_(p) with the slip error 148 results ina proportional increase in the value of the antiskid command 90 as theslip error 148 remains constant.

In block 208B, the control module 22 combines the slip error 148 withthe integral gain which results in a first integral value 164. Thecontrol module 22 also integrates the first integral value 164, whichresults in the second integral value 168. The method 200 may thenproceed to block 210.

In block 210, the control module 22 calculates the antiskid command 90based on the slip error 148, where the antiskid command 90 reduces anamount of brake pressure applied to the plurality of wheels 24. As seenin block 210A, the control module 22 determines the antiskid command 90by combining the proportional value 160 with the second integral value168. The method 200 may then proceed to block 212.

In block 212, the control module 22 determines the brake pressurecommand 88 based on a difference between the antiskid command 90 and theinput command 86, where the input command 86 represents an amount ofbraking requested by the brake system 18. The method 200 may then returnto block 204, or, alternatively the method 200 may terminate.

Turning now to FIG. 5, another approach to determine the brake pressurecommand 88 is now described. In the exemplary embodiment as shown inFIG. 5, the plurality of wheels 24 are part of a set of wheels 180. Forexample, in an embodiment, the set of wheels 24 are a set of landinggear for an aircraft 182. It is to be appreciated that some largeraircraft may include multiple sets of landing gear. For example, somelarger aircraft may include five sets of landing gears. In thenon-limiting embodiment as shown, the landing gear set includes fourwheels 24. Each wheel 24 is monitored by a corresponding wheel speedsensor 70.

Continuing to refer to FIG. 5, a single wheel 24 that is part of the setof wheels 24 is designated as an observer wheel 24A. The observer wheel24A is monitored to determine the mu-slip coefficient μ. Although thetop left wheel 24 is designated as the observer wheel 24A, it is to beappreciated that this illustration is merely exemplary in nature, andany of the wheels 24 may be designated as the observer wheel 24A. It isto be appreciated that each set of wheels 180 includes a correspondingdesignated observer wheel 24A. For example, an aircraft having five setsof landing gear would include five designated observer wheels 24A.

In response to determining the wheels 24 are rotating along a surface,the control module 22 determines a first brake pressure command 188 thatis only applied to the designed observer wheel 24A. It is to beappreciated that the first brake pressure command 188 is determinedbased on the ideal slip value. Specifically, referring to FIG. 3, thefirst brake pressure command 188 is determined based on the ideal slippoint 134 along the mu-slip curve 130, and not the target slip point136. Accordingly, the first brake pressure command 188 does not resultin a reduced braking efficiency 140 (seen in FIG. 3).

The control module 22 receives as input the wheel speed 80 from thewheel speed sensor 70A of the observer wheel 24A. The control module 22also receives the actual speed 102, such as a ground speed signal of theaircraft 182. The control module 22 determines a difference between thewheel speed 80 of the observer wheel 24A and the actual speed 102. Asexplained in greater detail below, the control module 22 determines whenthe observer wheel 24A starts to undergo a skid condition 190 (shown inFIG. 6C) based on the difference between the wheel speed 80 of theobserver wheel 24A and the actual speed 102. In response to detecting astart of the skid condition 190, the control module 22 decreases thefirst brake pressure command 188, which results in the observer wheel24A recovering from the skid condition 190. Once the observer wheel 24Ahas undergone at least one skid condition, then the control module 22calculates a second brake pressure command 189 that is applied to theremaining wheels 24 that are part of the set of wheels 180.

FIG. 6A illustrates a graph of a brake pressure 196 of the observerwheel 24A (i.e., the brake pressure signal 82 seen in FIG. 1) during theskid condition 190. FIGS. 6B and 6C illustrate a brake torque 198 of theobserver wheel 24A and the wheel speed 80 of the observer wheel 24A,respectively, during the skid condition 190. FIG. 6D illustrates anexemplary mu-slip curve 230 as the designed observer wheel 24A undergoesthe skid condition 190. The graphs shown in FIGS. 6A-6D each includefour operating points, which are labeled as operating point 1, operatingpoint 2, operating point 3, and operating point 4. As seen in FIG. 6A,the brake pressure 196 of the observer wheel 24A increases betweenoperating point 1, operating point 2, and operating point 3. As seen inFIG. 6C, the observer wheel 24A starts to undergo the skid condition 190between operating point 3 and operating point 4. However, the observerwheel 24A recovers from the skid condition 190 after operating point 4.

Referring to FIGS. 1, 5, 6A, and 6C, the control module 22 increases thevalue of the first brake pressure command 188, which results in anincreased brake pressure 196 of the observer wheel 24A (FIG. 6A). Thecontrol module 22 continues to increase the value of the first brakepressure command 188 until the skid condition 190 is detected (betweenoperating point 3 and operating point 4). An increase in the first brakepressure command 188 results in an increased amount of brake torque(seen in FIG. 6B) and a decrease in the wheel speed 80 of the observerwheel 24A (seen in FIG. 6C).

Referring to FIGS. 1, 5, 6A, and 6C, the control module 22 determinesthe start of the skid condition 190 based on the difference between thewheel speed 80 of the observer wheel 24A and the actual speed 102 of thevehicle 10 (i.e., ground speed of an aircraft). Specifically, thecontrol module 22 determines a difference in speed between the wheelspeed 80 of the observer wheel 24A and the actual speed 102 of thevehicle 10 (i.e., the ground speed of an aircraft). In response todetermining the difference in speed between the wheel speed 80 of theobserver wheel 24A and the actual speed 102 of the vehicle 10 exceeds athreshold difference, the control module 22 determines the designedobserver wheel 24A has started to undergo the skid condition 190. Thethreshold difference in speed represents a condition as the observerwheel 24A slips relative to a ground surface and undergoes a suddendecrease in speed. FIG. 6C illustrates the sudden decrease in the wheelspeed 80 of the observer wheel 24A during the skid condition 190.Specifically, FIG. 6C illustrates a line 300 connecting operating point3 and operating point 4 together and represents a sudden decrease inwheel speed 80 during the skid condition 190. A line 304 connectsoperating points 1, 2, and 3 together, and represents the wheel speed 80as the vehicle 10 comes to a stop before the skid condition 190. Thegradient of the line 300, which occurs as the observer wheel 24A isslipping during the skid condition 190, is at least twice the gradientof the line 304.

In response to detecting the start of the skid condition 190, thecontrol module 22 decreases the value of the first brake pressurecommand 188. Referring to FIGS. 5 and 6C, the control module 22continues to decrease the first brake pressure command 188 until theobserver wheel 24A recovers from the skid condition 190. As seen in FIG.6C, when the observer wheel 24A recovers from the skid condition 190,the wheel speed 80 of the observer wheel 24A is about equal to theactual speed 102 and is referred to as a skid recovery condition 240. Itis to be appreciated that while only one skid condition 190 is shown inFIG. 6C, the observer wheel 24A undergoes multiple skid conditions asthe aircraft 182 comes to a stop. However, only a single skid condition190 is illustrated in the graphs shown in FIGS. 6A-6C for purposes ofsimplicity.

Referring to FIG. 6D, the operating points 1, 2, 3, and 4 on the mu-slipcurve 230 correspond to operating points 1, 2, 3, and 4 in FIGS. 6A-6C.As mentioned above, the specific mu-slip curve 230 is based on empiricaldata and is dependent upon the specific type of tire 94 used by thedesigned observer wheel 24A (FIG. 5). It is to be appreciated that theobserver wheel 24A generates the ideal slip value as the observer wheel24A undergoes the skid condition. Specifically, with reference to FIGS.3, 5, 6C, and 6D, at operating point 4 on the mu-slip curve 230 (shownin FIG. 6D), the effective value of the mu-slip coefficient μ is at itsideal slip point 134. In other words, the mu-slip coefficient μ is atthe ideal slip point 134 when the observer wheel 24A undergoes the skidcondition 190. Referring specifically to FIGS. 3, 6C, and 6D, when thewheel speed 80 of the observer wheel 24A is at a minimum value (atoperating point 4), the effective value of the mu-slip coefficient μ isthe ideal slip point 134.

Referring to FIGS. 5 and 6A-6D, in response to determining the observerwheel 24A is starting the skid condition 190, the control module 22determines a second brake pressure command 189 applied to the remainingwheels 24. For example, in the embodiment as shown in FIG. 5, the secondbrake pressure command 189 would be applied to the remaining threewheels 24. The control module 22 determines the second brake pressurecommand 189 based on the target slip value 116, where the target slipvalue 116 is offset from the ideal slip value and results in a reducedbraking efficiency of the brake system 18. Specifically, as explainedabove and shown in FIG. 3, the target slip point 136 is offset from theideal slip point 134, and results in the reduced braking efficiency 140.The second brake pressure command 189 is them applied to the remainingplurality of wheels 24.

Referring to FIG. 5, in one embodiment the control module 22 determinesa reduced second brake pressure command 270 by reducing the second brakepressure command 189 by a parametric confidence value. The parametricconfidence value represents one or more varying operating conditionsbetween each wheel 24 of the set of wheels 180. In an embodiment, thevarying operating conditions include a coefficient of friction along aground surface, an amount of brake wear, an amount of tire wear, vehiclespeed during operation of the brake system 18, and brake torque gain.For example, one of the wheels 24 may experience a different coefficientof friction when compared to the remaining wheels 24. Specifically, oneof the wheels 24 may roll along a slippery or icy patch located alongthe runway while the other remaining wheels 24 roll along a dry portionof the runway. In one non-limiting embodiment, the parametric confidencevalue reduces the second brake pressure command 189 by about tenpercent, however, this value is exemplary in nature.

FIG. 7 is an exemplary process flow diagram illustrating a method 400for determining the second brake pressure command 189 that is applied tothe remaining wheels 24 of the aircraft 182 shown in FIG. 5. Referringgenerally to FIGS. 1, 5, 6A-6D, and 7, the method 400 begins at decisionblock 402. In decision block 402, the control module 22 determines ifthe brake system 18 is operating in the backup mode of operation. If thebrake system 18 is operating in the backup mode of operation, then themethod 400 may then proceed to block 404.

In block 204, in response to determining the brake system 18 isoperating in the backup mode of operation, the first brake pressurecommand 188 is applied to the observer wheel 24A (seen in FIG. 5). Themethod 400 may then proceed to block 406.

In block 406, the control module 22 monitors the wheel speed 80 of theobserver wheel and the actual speed 102 of the vehicle 182 as the firstbrake pressure command 188 is applied to the observer wheel 24A. If thevehicle 10 is an aircraft, such as the aircraft 182 seen in FIG. 5, thenthe actual speed 102 is the ground speed. Referring to FIGS. 5 and 6A,the control module 22 continues to increase a value of the first brakepressure command 188 while monitoring the wheel speed 80 of the observerwheel 24A and the actual speed 102 of the vehicle 10. The method 400 maythen proceed to decision block 408.

In decision block 408, the control module 22 determines if the observerwheel 24A is starting the skid condition 190 (seen in FIG. 6C) based onthe wheel speed 80 of the observer wheel 24A and the actual speed 102 ofthe vehicle 10. As seen in FIGS. 6C and 6D, the observer wheel 24Agenerates the ideal slip value (i.e., the ideal slip point 134) duringthe skid condition 190. For example, as explained above, the controlmodule 22 determines the designed observer wheel 24A has started toundergo the skid condition 190 in response to determining the differencebetween the wheel speed 80 of the observer wheel 24A and the actualspeed 102 exceeds the threshold difference.

If the observer wheel 24A is not starting the skid condition 190, thenthe method 400 returns to block 406. However, if the control module 22determines the observer wheel 24A is starting the skid condition basedon the wheel speed 80 of the observer wheel 24A and the actual speed 102of the vehicle 10, then the method 400 may proceed to blocks 410 and 414simultaneously.

In block 410, in response to determining the observer wheel 24A isstarting the skid condition 190, the control module 22 determines thesecond brake pressure command 189 based on the target slip value, wherethe target slip value is offset from the ideal slip value and results ina reduced braking efficiency of the brake system 18. The method 400 maythen proceed to block 412.

In block 412, the control module 22 applies the second brake pressurecommand 189 to the remaining portion of the plurality of wheels 24. Forexample, as seen in FIG. 5, the second brake pressure command 189 isapplied to the remaining three wheels 24.

Blocks 414 and 416 are now described. In block 414, in response todetermining the observer wheel 24A is starting the skid condition 190,the control module 22 decreases the value of the first brake pressurecommand 188. The method 400 may then proceed to decision block 416.

In decision block 416, the control module 22 determines if the wheelspeed 80 of the observer wheel 24A is about equal to the actual speed102 of the vehicle 10. If the wheel speed 80 is not about equal to theactual speed 102, then the method returns to block 414, and the firstbrake pressure command 188 continues to decrease. However, if the wheelspeed 80 of the observer wheel 24A is about the same as the actual speed102 of the vehicle 10, then the skid recovery condition 240 (seen inFIG. 6C) is achieved. The method may then return to block 404, whereanother skid condition 190 is re-created. Alternatively, if the vehicle10 has come to a stop, then the method 400 may terminate.

Referring generally to FIGS. 1-7, the present disclosure providesvarious technical effects and benefits for an energy storage device of abrake system. Specifically, the disclosed brake system utilizes lessenergy each time brakes are applied during the backup mode of operationwhen compared to a conventional brake system, which conserves the energystored within the energy storage device. Accordingly, in someapproaches, the disclosed energy storage device may be smaller andlighter when compared to conventional devices, which in turn reduces themass of a vehicle such as an aircraft.

Referring now to FIG. 8, the control module 22 is implemented on one ormore computer devices or systems, such as exemplary computer system1030. The computer system 1030 includes a processor 1032, a memory 1034,a mass storage memory device 1036, an input/output (I/O) interface 1038,and a Human Machine Interface (HMI) 1040. The computer system 1030 isoperatively coupled to one or more external resources 1042 via thenetwork 1026 or I/O interface 1038. External resources may include, butare not limited to, servers, databases, mass storage devices, peripheraldevices, cloud-based network services, or any other suitable computerresource that may be used by the computer system 1030.

The processor 1032 includes one or more devices selected frommicroprocessors, micro-controllers, digital signal processors,microcomputers, central processing units, field programmable gatearrays, programmable logic devices, state machines, logic circuits,analog circuits, digital circuits, or any other devices that manipulatesignals (analog or digital) based on operational instructions that arestored in the memory 1034. Memory 1034 includes a single memory deviceor a plurality of memory devices including, but not limited to,read-only memory (ROM), random access memory (RAM), volatile memory,non-volatile memory, static random-access memory (SRAM), dynamicrandom-access memory (DRAM), flash memory, cache memory, or any otherdevice capable of storing information. The mass storage memory device1036 includes data storage devices such as a hard drive, optical drive,tape drive, volatile or non-volatile solid-state device, or any otherdevice capable of storing information.

The processor 1032 operates under the control of an operating system1046 that resides in memory 1034. The operating system 1046 managescomputer resources so that computer program code embodied as one or morecomputer software applications, such as an application 1048 residing inmemory 1034, may have instructions executed by the processor 1032. In analternative example, the processor 1032 may execute the application 1048directly, in which case the operating system 1046 may be omitted. One ormore data structures 1049 also reside in memory 1034, and may be used bythe processor 1032, operating system 1046, or application 1048 to storeor manipulate data.

The I/O interface 1038 provides a machine interface that operativelycouples the processor 1032 to other devices and systems, such as thenetwork 1026 or external resource 1042. The application 1048 therebyworks cooperatively with the network 1026 or external resource 1042 bycommunicating via the I/O interface 1038 to provide the variousfeatures, functions, applications, processes, or modules comprisingexamples of the disclosure. The application 1048 also includes programcode that is executed by one or more external resources 1042, orotherwise rely on functions or signals provided by other system ornetwork components external to the computer system 1030. Indeed, giventhe nearly endless hardware and software configurations possible,persons having ordinary skill in the art will understand that examplesof the disclosure may include applications that are located externallyto the computer system 1030, distributed among multiple computers orother external resources 1042, or provided by computing resources(hardware and software) that are provided as a service over the network1026, such as a cloud computing service.

The HMI 1040 is operatively coupled to the processor 1032 of computersystem 1030 in a known manner to allow a user to interact directly withthe computer system 1030. The HMI 1040 may include video or alphanumericdisplays, a touch screen, a speaker, and any other suitable audio andvisual indicators capable of providing data to the user. The HMI 1040also includes input devices and controls such as an alphanumerickeyboard, a pointing device, keypads, pushbuttons, control knobs,microphones, etc., capable of accepting commands or input from the userand transmitting the entered input to the processor 1032.

A database 1044 may reside on the mass storage memory device 1036 andmay be used to collect and organize data used by the various systems andmodules described herein. The database 1044 may include data andsupporting data structures that store and organize the data. Inparticular, the database 1044 may be arranged with any databaseorganization or structure including, but not limited to, a relationaldatabase, a hierarchical database, a network database, or combinationsthereof. A database management system in the form of a computer softwareapplication executing as instructions on the processor 1032 may be usedto access the information or data stored in records of the database 1044in response to a query, where a query may be dynamically determined andexecuted by the operating system 1046, other applications 1048, or oneor more modules.

The description of the present disclosure is merely exemplary in natureand variations that do not depart from the gist of the presentdisclosure are intended to be within the scope of the presentdisclosure. Such variations are not to be regarded as a departure fromthe spirit and scope of the present disclosure.

What is claimed is:
 1. A brake system for a vehicle, wherein the brakesystem includes an energy storage device configured to store anddischarge energy and a plurality of wheels, the brake system comprising:one or more processors operatively coupled to the energy storage deviceand in electrical communication with the plurality of wheels; and amemory coupled to the one or more processors, the memory storing datacomprising a database and program code that, when executed by the one ormore processors, causes the brake system to: determine the brake systemis operating in a backup mode of operation; in response to determiningthe brake system is operating in the backup mode of operation, calculatea dynamic slip of the plurality of wheels; determine a slip error bycomparing the dynamic slip with a target slip value of the plurality ofwheels, wherein the target slip value is offset from an ideal slip valueof the plurality of wheels, results in a reduced braking efficiency ofthe brake system, is a fixed value based on a type of tire installed onthe plurality of wheels, and is saved in the memory of the one or moreprocessors; select the target slip value resulting in the brake systemhaving the vehicle come to a stop within a threshold time and athreshold distance; and calculate an antiskid command based on the sliperror, wherein the antiskid command reduces an amount of brake pressureapplied to the plurality of wheels.
 2. The brake system of claim 1,wherein the one or more processors execute instructions to: determinethe slip error based on a wheel frequency of the plurality of wheels andan actual speed of the vehicle.
 3. The brake system of claim 2, whereinthe one or more processors execute instructions to determine the sliperror based on:${{Dynamic}\mspace{14mu}{slip}} = \frac{( {{{actual}\mspace{14mu}{speed}\mspace{14mu}{signal}} - {R*\omega}} )}{{actual}\mspace{14mu}{speed}\mspace{14mu}{signal}}$wherein R represents a tire rolling radius of the plurality of wheels ofthe vehicle and ω represents the wheel frequency of the plurality ofwheels.
 4. The brake system of claim 1, wherein the one or moreprocessors execute instructions to: determine a proportional value bycombining the slip error with a proportional gain, wherein combining theproportional gain with the slip error results in a proportional increasein a value of the antiskid command as the slip error remains constant.5. The brake system of claim 4, wherein the one or more processorsexecute instructions to: determine a first integral value by combing theslip error with an integral gain value; and integrate the first integralvalue, which results in a second integral value.
 6. The brake system ofclaim 5, wherein the one or more processors execute instructions to:determine the antiskid command by combining the proportional value withthe second integral value.
 7. The brake system of claim 1, wherein theone or more processors execute instructions to: determine a brakepressure command based on a difference between the antiskid command andan input command, wherein the input command represents an amount ofbraking requested by the brake system.
 8. The brake system of claim 1,wherein the energy storage device is an accumulator, a battery, acapacitor, or a flywheel.
 9. The brake system of claim 1, wherein thetype of tire depends on characteristics including belt construction andsidewall construction, and wherein the belt construction refers toeither a radial or cross-ply construction.
 10. An aircraft, comprising:a brake system including a plurality of wheels and an accumulator,wherein the accumulator is configured to store and discharge fluidenergy as a pressurized hydraulic brake fluid; one or more processorsoperatively coupled to the accumulator and in electrical communicationwith the plurality of wheels; and a memory coupled to the one or moreprocessors, the memory storing data comprising a database and programcode that, when executed by the one or more processors, causes the brakesystem to: determine the brake system is operating in a backup mode ofoperation, wherein the backup mode of operation conserves the fluidenergy stored in the accumulator; in response to determining the brakesystem is operating in the backup mode of operation, calculate a dynamicslip of the plurality of wheels; determine a slip error by comparing thedynamic slip with a target slip value of the plurality of wheels,wherein the target slip value is offset from an ideal slip value of theplurality of wheels, results in a reduced braking efficiency of thebrake system, is a fixed value based on a type of tire installed on theplurality of wheels, and is saved in the memory of the one or moreprocessors; select the target slip value resulting in the brake systemhaving the aircraft come to a stop within a threshold time and athreshold distance; and calculate an antiskid command based on the sliperror, wherein the antiskid command reduces an amount of brake pressureapplied to the plurality of wheels.
 11. The aircraft of claim 10,wherein the one or more processors execute instructions to: determinethe slip error based on a wheel frequency of the plurality of wheels andan actual speed of the aircraft.
 12. The aircraft of claim 11, whereinthe one or more processors execute instructions to determine the sliperror based on:${{Dynamic}\mspace{14mu}{slip}} = \frac{( {{{actual}\mspace{14mu}{speed}\mspace{14mu}{signal}} - {R*\omega}} )}{{actual}\mspace{14mu}{speed}\mspace{14mu}{signal}}$wherein R represents a tire rolling radius of the plurality of wheels ofthe aircraft and ω represents the wheel frequency of the plurality ofwheels.
 13. The aircraft of claim 10, wherein the one or more processorsexecute instructions to: determine a proportional value by combining theslip error with a proportional gain, wherein combining the proportionalgain with the slip error results in a proportional increase in a valueof the antiskid command as the slip error remains constant.
 14. Theaircraft of claim 13, wherein the one or more processors executeinstructions to: determine a first integral value by combing the sliperror with an integral gain value; and integrate the first integralvalue, which results in a second integral value.
 15. The aircraft ofclaim 14, wherein the one or more processors execute instructions to:determine the antiskid command by combining the proportional value withthe second integral value.
 16. The aircraft of claim 10, wherein the oneor more processors execute instructions to: determine a brake pressurecommand based on a difference between the antiskid command and an inputcommand, wherein the input command represents an amount of brakingrequested by the brake system.
 17. A method of determining an antiskidcommand during a backup mode of operation for a brake system of avehicle, wherein the brake system includes a plurality of wheels andenergy storage device configured to store and discharge energy, themethod comprising: determining, by a computer, the brake system isoperating in a backup mode of operation; in response to determining thebrake system is operating in the backup mode of operation, calculating,by the computer, a dynamic slip of the plurality of wheels; determininga slip error by comparing the dynamic slip with a target slip value,wherein the target slip value is less than an ideal slip value resultsin a reduction in braking efficiency when compared to the ideal slipvalue, is a fixed value based on a type of tire installed on theplurality of wheels, and is saved in a memory of the computer; selectingthe target slip value resulting in the brake system having the vehiclecome to a stop within a threshold time and a threshold distance; andcalculating an antiskid command based on the slip error, wherein theantiskid command reduces an amount of brake pressure applied to theplurality of wheels.
 18. The method of claim 17, further comprising:determining the slip error based on a wheel frequency of the pluralityof wheels and an actual speed of the vehicle.
 19. The method of claim18, further comprising determining the dynamic slip based on:${{Dynamic}\mspace{14mu}{slip}} = \frac{( {{{actual}\mspace{14mu}{speed}\mspace{14mu}{of}\mspace{14mu}{the}\mspace{14mu}{vehicle}} - {R*\omega}} )}{{actual}\mspace{14mu}{speed}\mspace{14mu}{signal}}$wherein R represents a tire rolling radius of the plurality of wheels ofthe vehicle and ω represents the wheel frequency of the plurality ofwheels.
 20. The method of claim 17, further comprising: determining abrake pressure command based on a difference between the antiskidcommand and an input command, wherein the input command represents anamount of braking requested by the brake system.